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3 Commits

Author SHA1 Message Date
Sungun Park
7017bde04d Optimize thread variables in ServiceThread
Wraps thread-related member variables in preprocessor checks to ensure
they are excluded when multithreading is not supported. Previously,
these variables were declared unconditionally, leading to unnecessary
memory usage for platforms that don't support multithreading.
2026-01-20 07:42:15 -08:00
Sungun Park
7701e7a65a Handle deferred destruction for asynchronous objects (#9604)
When an asynchronous object is destroyed immediately after creation, the
background creation process may still be active, holding a reference to
the object. We now defer destruction in these cases until the creation
process completes to ensure the reference remains valid.

Implementation details:
1. Add a mechanism to stop the ServiceThread to drain pending
   asynchronous tasks earlier. This ensures the mCreationComplete flag
   in the frontend object is set to true.
2. Later, the engine's terminate performs garbage collection for the
   deferred destruction. All of them must be successfully processed.

BUGS=[442921995]
2026-01-17 02:44:28 +00:00
Filament Bot
65a91832a8 [automated] Updating /docs due to commit acb47ff
Full commit hash is acb47ffed5

DOCS_ALLOW_DIRECT_EDITS
2026-01-16 00:26:35 +00:00
10 changed files with 360 additions and 254 deletions

View File

@@ -181,7 +181,7 @@ important for <code>matc</code> (material compiler).</p>
}
dependencies {
implementation 'com.google.android.filament:filament-android:1.68.3'
implementation 'com.google.android.filament:filament-android:1.68.4'
}
</code></pre>
<p>Here are all the libraries available in the group <code>com.google.android.filament</code>:</p>
@@ -196,7 +196,7 @@ dependencies {
</div>
<h3 id="ios"><a class="header" href="#ios">iOS</a></h3>
<p>iOS projects can use CocoaPods to install the latest release:</p>
<pre><code class="language-shell">pod 'Filament', '~&gt; 1.68.3'
<pre><code class="language-shell">pod 'Filament', '~&gt; 1.68.4'
</code></pre>
<h2 id="documentation"><a class="header" href="#documentation">Documentation</a></h2>
<ul>

View File

@@ -504,9 +504,9 @@ D_{GGX}(h,\alpha) = \frac{\aa}{\pi ( (\NoH)^2 (\aa - 1) + 1)^2}
\end{equation}$$
</p><p>
The GLSL implementation of the NDF, shown in <a href="#listing_speculard">listing&nbsp;1</a>, is simple and efficient.
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-built_in">float</span> <span class="hljs-title">D_GGX</span>(<span class="hljs-params"><span class="hljs-built_in">float</span> NoH, <span class="hljs-built_in">float</span> roughness</span>)</span> {</span>
<span class="line"> <span class="hljs-built_in">float</span> a = NoH * roughness;</span>
<span class="line"> <span class="hljs-built_in">float</span> k = roughness / (<span class="hljs-number">1.0</span> - NoH * NoH + a * a);</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-type">float</span> <span class="hljs-title">D_GGX</span><span class="hljs-params">(<span class="hljs-type">float</span> NoH, <span class="hljs-type">float</span> roughness)</span> </span>{</span>
<span class="line"> <span class="hljs-type">float</span> a = NoH * roughness;</span>
<span class="line"> <span class="hljs-type">float</span> k = roughness / (<span class="hljs-number">1.0</span> - NoH * NoH + a * a);</span>
<span class="line"> <span class="hljs-keyword">return</span> k * k * (<span class="hljs-number">1.0</span> / PI);</span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_speculard">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;1:</b> Implementation of the specular D term in GLSL</div></center>
<p>
@@ -590,10 +590,10 @@ V(v,l,\alpha) = \frac{0.5}{\NoL \sqrt{(\NoV)^2 (1 - \aa) + \aa} + \NoV \sqrt{(\N
\end{equation}$$
</p><p>
The GLSL implementation of the visibility term, shown in <a href="#listing_specularv">listing&nbsp;3</a>, is a bit more expensive than we would like since it requires two <code>sqrt</code> operations.
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-keyword">float</span> <span class="hljs-title">V_SmithGGXCorrelated</span><span class="hljs-params">(<span class="hljs-keyword">float</span> NoV, <span class="hljs-keyword">float</span> NoL, <span class="hljs-keyword">float</span> roughness)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">float</span> a2 = roughness * roughness;</span>
<span class="line"> <span class="hljs-keyword">float</span> GGXV = NoL * <span class="hljs-built_in">sqrt</span>(NoV * NoV * (<span class="hljs-number">1.0</span> - a2) + a2);</span>
<span class="line"> <span class="hljs-keyword">float</span> GGXL = NoV * <span class="hljs-built_in">sqrt</span>(NoL * NoL * (<span class="hljs-number">1.0</span> - a2) + a2);</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-type">float</span> <span class="hljs-title">V_SmithGGXCorrelated</span><span class="hljs-params">(<span class="hljs-type">float</span> NoV, <span class="hljs-type">float</span> NoL, <span class="hljs-type">float</span> roughness)</span> </span>{</span>
<span class="line"> <span class="hljs-type">float</span> a2 = roughness * roughness;</span>
<span class="line"> <span class="hljs-type">float</span> GGXV = NoL * <span class="hljs-built_in">sqrt</span>(NoV * NoV * (<span class="hljs-number">1.0</span> - a2) + a2);</span>
<span class="line"> <span class="hljs-type">float</span> GGXL = NoV * <span class="hljs-built_in">sqrt</span>(NoL * NoL * (<span class="hljs-number">1.0</span> - a2) + a2);</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">0.5</span> / (GGXV + GGXL);</span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_specularv">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;3:</b> Implementation of the specular V term in GLSL</div></center>
<p>
@@ -604,10 +604,10 @@ V(v,l,\alpha) = \frac{0.5}{\NoL (\NoV (1 - \alpha) + \alpha) + \NoV (\NoL (1 - \
\end{equation}$$
</p><p>
This approximation is mathematically wrong but saves two square root operations and is good enough for real-time mobile applications, as shown in <a href="#listing_approximatedspecularv">listing&nbsp;4</a>.
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-built_in">float</span> <span class="hljs-title">V_SmithGGXCorrelatedFast</span>(<span class="hljs-params"><span class="hljs-built_in">float</span> NoV, <span class="hljs-built_in">float</span> NoL, <span class="hljs-built_in">float</span> roughness</span>)</span> {</span>
<span class="line"> <span class="hljs-built_in">float</span> a = roughness;</span>
<span class="line"> <span class="hljs-built_in">float</span> GGXV = NoL * (NoV * (<span class="hljs-number">1.0</span> - a) + a);</span>
<span class="line"> <span class="hljs-built_in">float</span> GGXL = NoV * (NoL * (<span class="hljs-number">1.0</span> - a) + a);</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-type">float</span> <span class="hljs-title">V_SmithGGXCorrelatedFast</span><span class="hljs-params">(<span class="hljs-type">float</span> NoV, <span class="hljs-type">float</span> NoL, <span class="hljs-type">float</span> roughness)</span> </span>{</span>
<span class="line"> <span class="hljs-type">float</span> a = roughness;</span>
<span class="line"> <span class="hljs-type">float</span> GGXV = NoL * (NoV * (<span class="hljs-number">1.0</span> - a) + a);</span>
<span class="line"> <span class="hljs-type">float</span> GGXL = NoV * (NoL * (<span class="hljs-number">1.0</span> - a) + a);</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">0.5</span> / (GGXV + GGXL);</span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_approximatedspecularv">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;4:</b> Implementation of the approximated specular V term in GLSL</div></center>
<p>
@@ -659,7 +659,7 @@ $$\begin{equation}
\end{equation}$$
</p><p>
In practice, the diffuse reflectance \(\sigma\) is multiplied later, as shown in <a href="#listing_diffusebrdf">listing&nbsp;8</a>.
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-built_in">float</span> <span class="hljs-title">Fd_Lambert</span>(<span class="hljs-params"></span>)</span> {</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-built_in">float</span> <span class="hljs-title">Fd_Lambert</span>()</span> {</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">1.0</span> / PI;</span>
<span class="line">}</span>
<span class="line"></span>
@@ -680,14 +680,14 @@ Where:
$$\begin{equation}
\fGrazing=0.5 + 2 \cdot \alpha cos^2(\theta_d)
\end{equation}$$
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-keyword">float</span> <span class="hljs-title">F_Schlick</span><span class="hljs-params">(<span class="hljs-keyword">float</span> u, <span class="hljs-keyword">float</span> f0, <span class="hljs-keyword">float</span> f90)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">return</span> f0 + (f90 - f0) * <span class="hljs-built_in">pow</span>(<span class="hljs-number">1.0</span> - u, <span class="hljs-number">5.0</span>);</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-type">float</span> <span class="hljs-title function_">F_Schlick</span><span class="hljs-params">(<span class="hljs-type">float</span> u, <span class="hljs-type">float</span> f0, <span class="hljs-type">float</span> f90)</span> {</span>
<span class="line"> <span class="hljs-keyword">return</span> f0 + (f90 - f0) * pow(<span class="hljs-number">1.0</span> - u, <span class="hljs-number">5.0</span>);</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-function"><span class="hljs-keyword">float</span> <span class="hljs-title">Fd_Burley</span><span class="hljs-params">(<span class="hljs-keyword">float</span> NoV, <span class="hljs-keyword">float</span> NoL, <span class="hljs-keyword">float</span> LoH, <span class="hljs-keyword">float</span> roughness)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">float</span> f90 = <span class="hljs-number">0.5</span> + <span class="hljs-number">2.0</span> * roughness * LoH * LoH;</span>
<span class="line"> <span class="hljs-keyword">float</span> lightScatter = F_Schlick(NoL, <span class="hljs-number">1.0</span>, f90);</span>
<span class="line"> <span class="hljs-keyword">float</span> viewScatter = F_Schlick(NoV, <span class="hljs-number">1.0</span>, f90);</span>
<span class="line"><span class="hljs-type">float</span> <span class="hljs-title function_">Fd_Burley</span><span class="hljs-params">(<span class="hljs-type">float</span> NoV, <span class="hljs-type">float</span> NoL, <span class="hljs-type">float</span> LoH, <span class="hljs-type">float</span> roughness)</span> {</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">f90</span> <span class="hljs-operator">=</span> <span class="hljs-number">0.5</span> + <span class="hljs-number">2.0</span> * roughness * LoH * LoH;</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">lightScatter</span> <span class="hljs-operator">=</span> F_Schlick(NoL, <span class="hljs-number">1.0</span>, f90);</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">viewScatter</span> <span class="hljs-operator">=</span> F_Schlick(NoV, <span class="hljs-number">1.0</span>, f90);</span>
<span class="line"> <span class="hljs-keyword">return</span> lightScatter * viewScatter * (<span class="hljs-number">1.0</span> / PI);</span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_diffusebrdf">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;8:</b> Implementation of the diffuse Disney BRDF in GLSL</div></center>
<p>
@@ -704,47 +704,47 @@ We could allow artists/developers to choose the Disney diffuse BRDF depending on
<strong class="asterisk">Diffuse term</strong>: a Lambertian diffuse model.
</p><p>
The full GLSL implementation of the standard model is shown in <a href="#listing_glslbrdf">listing&nbsp;9</a>.
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-type">float</span> D_GGX(<span class="hljs-type">float</span> NoH, <span class="hljs-type">float</span> a) {</span>
<span class="line"> <span class="hljs-type">float</span> a2 = a * a;</span>
<span class="line"> <span class="hljs-type">float</span> f = (NoH * a2 - NoH) * NoH + <span class="hljs-number">1.0</span>;</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-type">float</span> <span class="hljs-title function_">D_GGX</span><span class="hljs-params">(<span class="hljs-type">float</span> NoH, <span class="hljs-type">float</span> a)</span> {</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">a2</span> <span class="hljs-operator">=</span> a * a;</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">f</span> <span class="hljs-operator">=</span> (NoH * a2 - NoH) * NoH + <span class="hljs-number">1.0</span>;</span>
<span class="line"> <span class="hljs-keyword">return</span> a2 / (PI * f * f);</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-type">vec3</span> F_Schlick(<span class="hljs-type">float</span> u, <span class="hljs-type">vec3</span> f0) {</span>
<span class="line"> <span class="hljs-keyword">return</span> f0 + (<span class="hljs-type">vec3</span>(<span class="hljs-number">1.0</span>) - f0) * <span class="hljs-built_in">pow</span>(<span class="hljs-number">1.0</span> - u, <span class="hljs-number">5.0</span>);</span>
<span class="line">vec3 <span class="hljs-title function_">F_Schlick</span><span class="hljs-params">(<span class="hljs-type">float</span> u, vec3 f0)</span> {</span>
<span class="line"> <span class="hljs-keyword">return</span> f0 + (vec3(<span class="hljs-number">1.0</span>) - f0) * pow(<span class="hljs-number">1.0</span> - u, <span class="hljs-number">5.0</span>);</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-type">float</span> V_SmithGGXCorrelated(<span class="hljs-type">float</span> NoV, <span class="hljs-type">float</span> NoL, <span class="hljs-type">float</span> a) {</span>
<span class="line"> <span class="hljs-type">float</span> a2 = a * a;</span>
<span class="line"> <span class="hljs-type">float</span> GGXL = NoV * <span class="hljs-built_in">sqrt</span>((-NoL * a2 + NoL) * NoL + a2);</span>
<span class="line"> <span class="hljs-type">float</span> GGXV = NoL * <span class="hljs-built_in">sqrt</span>((-NoV * a2 + NoV) * NoV + a2);</span>
<span class="line"><span class="hljs-type">float</span> <span class="hljs-title function_">V_SmithGGXCorrelated</span><span class="hljs-params">(<span class="hljs-type">float</span> NoV, <span class="hljs-type">float</span> NoL, <span class="hljs-type">float</span> a)</span> {</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">a2</span> <span class="hljs-operator">=</span> a * a;</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">GGXL</span> <span class="hljs-operator">=</span> NoV * sqrt((-NoL * a2 + NoL) * NoL + a2);</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">GGXV</span> <span class="hljs-operator">=</span> NoL * sqrt((-NoV * a2 + NoV) * NoV + a2);</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">0.5</span> / (GGXV + GGXL);</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-type">float</span> Fd_Lambert() {</span>
<span class="line"><span class="hljs-type">float</span> <span class="hljs-title function_">Fd_Lambert</span><span class="hljs-params">()</span> {</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">1.0</span> / PI;</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-type">void</span> BRDF(...) {</span>
<span class="line"> <span class="hljs-type">vec3</span> h = <span class="hljs-built_in">normalize</span>(v + l);</span>
<span class="line"><span class="hljs-keyword">void</span> <span class="hljs-title function_">BRDF</span><span class="hljs-params">(...)</span> {</span>
<span class="line"> <span class="hljs-type">vec3</span> <span class="hljs-variable">h</span> <span class="hljs-operator">=</span> normalize(v + l);</span>
<span class="line"></span>
<span class="line"> <span class="hljs-type">float</span> NoV = <span class="hljs-built_in">abs</span>(<span class="hljs-built_in">dot</span>(n, v)) + <span class="hljs-number">1e-5</span>;</span>
<span class="line"> <span class="hljs-type">float</span> NoL = <span class="hljs-built_in">clamp</span>(<span class="hljs-built_in">dot</span>(n, l), <span class="hljs-number">0.0</span>, <span class="hljs-number">1.0</span>);</span>
<span class="line"> <span class="hljs-type">float</span> NoH = <span class="hljs-built_in">clamp</span>(<span class="hljs-built_in">dot</span>(n, h), <span class="hljs-number">0.0</span>, <span class="hljs-number">1.0</span>);</span>
<span class="line"> <span class="hljs-type">float</span> LoH = <span class="hljs-built_in">clamp</span>(<span class="hljs-built_in">dot</span>(l, h), <span class="hljs-number">0.0</span>, <span class="hljs-number">1.0</span>);</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">NoV</span> <span class="hljs-operator">=</span> abs(dot(n, v)) + <span class="hljs-number">1e-5</span>;</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">NoL</span> <span class="hljs-operator">=</span> clamp(dot(n, l), <span class="hljs-number">0.0</span>, <span class="hljs-number">1.0</span>);</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">NoH</span> <span class="hljs-operator">=</span> clamp(dot(n, h), <span class="hljs-number">0.0</span>, <span class="hljs-number">1.0</span>);</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">LoH</span> <span class="hljs-operator">=</span> clamp(dot(l, h), <span class="hljs-number">0.0</span>, <span class="hljs-number">1.0</span>);</span>
<span class="line"></span>
<span class="line"> <span class="hljs-comment">// perceptually linear roughness to roughness (see parameterization)</span></span>
<span class="line"> <span class="hljs-type">float</span> roughness = perceptualRoughness * perceptualRoughness;</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">roughness</span> <span class="hljs-operator">=</span> perceptualRoughness * perceptualRoughness;</span>
<span class="line"></span>
<span class="line"> <span class="hljs-type">float</span> D = D_GGX(NoH, roughness);</span>
<span class="line"> <span class="hljs-type">vec3</span> F = F_Schlick(LoH, f0);</span>
<span class="line"> <span class="hljs-type">float</span> V = V_SmithGGXCorrelated(NoV, NoL, roughness);</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">D</span> <span class="hljs-operator">=</span> D_GGX(NoH, roughness);</span>
<span class="line"> <span class="hljs-type">vec3</span> <span class="hljs-variable">F</span> <span class="hljs-operator">=</span> F_Schlick(LoH, f0);</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">V</span> <span class="hljs-operator">=</span> V_SmithGGXCorrelated(NoV, NoL, roughness);</span>
<span class="line"></span>
<span class="line"> <span class="hljs-comment">// specular BRDF</span></span>
<span class="line"> <span class="hljs-type">vec3</span> Fr = (D * V) * F;</span>
<span class="line"> <span class="hljs-type">vec3</span> <span class="hljs-variable">Fr</span> <span class="hljs-operator">=</span> (D * V) * F;</span>
<span class="line"></span>
<span class="line"> <span class="hljs-comment">// diffuse BRDF</span></span>
<span class="line"> <span class="hljs-type">vec3</span> Fd = diffuseColor * Fd_Lambert();</span>
<span class="line"> <span class="hljs-type">vec3</span> <span class="hljs-variable">Fd</span> <span class="hljs-operator">=</span> diffuseColor * Fd_Lambert();</span>
<span class="line"></span>
<span class="line"> <span class="hljs-comment">// apply lighting...</span></span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_glslbrdf">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;9:</b> Evaluation of the BRDF in GLSL</div></center>
@@ -965,7 +965,7 @@ $$\begin{equation}
\end{equation}$$
</p><p>
<a href="#listing_fnormal">Listing&nbsp;12</a> shows how \(\fNormal\) is computed for both dielectric and metallic materials. It shows that the color of the specular reflectance is derived from the base color in the metallic case.
</p><pre class="listing tilde"><code><span class="line">vec3 f0 = 0.16 <span class="hljs-emphasis">* reflectance *</span> reflectance <span class="hljs-emphasis">* (1.0 - metallic) + baseColor *</span> metallic;</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_fnormal">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;12:</b> Computing \(\fNormal\) for dielectric and metallic materials in GLSL</div></center>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-symbol">vec3</span> <span class="hljs-built_in">f0</span> = <span class="hljs-number">0</span>.<span class="hljs-number">16</span> * reflectance * reflectance * (<span class="hljs-number">1</span>.<span class="hljs-number">0</span> - metallic) + baseColor * metallic<span class="hljs-comment">;</span></span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_fnormal">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;12:</b> Computing \(\fNormal\) for dielectric and metallic materials in GLSL</div></center>
<a class="target" name="roughnessremappingandclamping">&nbsp;</a><a class="target" name="materialsystem/parameterization/remapping/roughnessremappingandclamping">&nbsp;</a><a class="target" name="toc4.8.3.3">&nbsp;</a><h4 id="roughness-remapping-and-clamping"><a class="header" href="#roughness-remapping-and-clamping">Roughness remapping and clamping</a></h4>
<p>
<p>The roughness set by the user, called <code>perceptualRoughness</code> here, is remapped to a perceptually linear range using the following formulation:</p>
@@ -1054,7 +1054,7 @@ V(l,h) = \frac{1}{4(\LoH)^2}
This masking-shadowing function is not physically based, as shown in [<a href="#citation-heitz14">Heitz14</a>], but its simplicity makes it desirable for real-time rendering.
</p><p>
In summary, our clear coat BRDF is a Cook-Torrance specular microfacet model, with a GGX normal distribution function, a Kelemen visibility function, and a Schlick Fresnel function. <a href="#listing_kelemen">Listing&nbsp;13</a> shows how trivial the GLSL implementation is.
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-built_in">float</span> <span class="hljs-title">V_Kelemen</span>(<span class="hljs-params"><span class="hljs-built_in">float</span> LoH</span>)</span> {</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-type">float</span> <span class="hljs-title">V_Kelemen</span><span class="hljs-params">(<span class="hljs-type">float</span> LoH)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">0.25</span> / (LoH * LoH);</span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_kelemen">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;13:</b> Implementation of the Kelemen visibility term in GLSL</div></center>
<p>
@@ -1097,18 +1097,18 @@ The clear coat roughness parameter is remapped and clamped in a similar way to t
<center><div class="image" style=""><a href="../images/material_clear_coat2.png" target="_blank"><img class="markdeep" src="../images/material_clear_coat2.png" /></a><center><span class="imagecaption"><a class="target" name="figure_clearcoatroughness">&nbsp;</a><b style="font-style:normal;">Figure&nbsp;26:</b> Clear coat roughness varying from 0.0 (left) to 1.0 (right) with metallic set to 1.0, roughness to 0.8 and clear coat to 1.0</span></center></div></center>
</p><p>
<a href="#listing_clearcoatbrdf">Listing&nbsp;14</a> shows the GLSL implementation of the clear coat material model after remapping, parameterization and integration in the standard surface response.
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">BRDF</span>(<span class="hljs-params">...</span>)</span> {</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-type">void</span> <span class="hljs-title">BRDF</span><span class="hljs-params">(...)</span> </span>{</span>
<span class="line"> <span class="hljs-comment">// compute Fd and Fr from standard model</span></span>
<span class="line"></span>
<span class="line"> <span class="hljs-comment">// remapping and linearization of clear coat roughness</span></span>
<span class="line"> clearCoatPerceptualRoughness = clamp(clearCoatPerceptualRoughness, <span class="hljs-number">0.089</span>, <span class="hljs-number">1.0</span>);</span>
<span class="line"> clearCoatPerceptualRoughness = <span class="hljs-built_in">clamp</span>(clearCoatPerceptualRoughness, <span class="hljs-number">0.089</span>, <span class="hljs-number">1.0</span>);</span>
<span class="line"> clearCoatRoughness = clearCoatPerceptualRoughness * clearCoatPerceptualRoughness;</span>
<span class="line"></span>
<span class="line"> <span class="hljs-comment">// clear coat BRDF</span></span>
<span class="line"> <span class="hljs-built_in">float</span> Dc = D_GGX(clearCoatRoughness, NoH);</span>
<span class="line"> <span class="hljs-built_in">float</span> Vc = V_Kelemen(clearCoatRoughness, LoH);</span>
<span class="line"> <span class="hljs-built_in">float</span> Fc = F_Schlick(<span class="hljs-number">0.04</span>, LoH) * clearCoat; <span class="hljs-comment">// clear coat strength</span></span>
<span class="line"> <span class="hljs-built_in">float</span> Frc = (Dc * Vc) * Fc;</span>
<span class="line"> <span class="hljs-type">float</span> Dc = <span class="hljs-built_in">D_GGX</span>(clearCoatRoughness, NoH);</span>
<span class="line"> <span class="hljs-type">float</span> Vc = <span class="hljs-built_in">V_Kelemen</span>(clearCoatRoughness, LoH);</span>
<span class="line"> <span class="hljs-type">float</span> Fc = <span class="hljs-built_in">F_Schlick</span>(<span class="hljs-number">0.04</span>, LoH) * clearCoat; <span class="hljs-comment">// clear coat strength</span></span>
<span class="line"> <span class="hljs-type">float</span> Frc = (Dc * Vc) * Fc;</span>
<span class="line"></span>
<span class="line"> <span class="hljs-comment">// account for energy loss in the base layer</span></span>
<span class="line"> <span class="hljs-keyword">return</span> color * ((Fd + Fr * (<span class="hljs-number">1.0</span> - Fc)) * (<span class="hljs-number">1.0</span> - Fc) + Frc);</span>
@@ -1294,14 +1294,14 @@ f_{r}(v,h,\alpha) = \frac{D_{velvet}(v,h,\alpha)}{4(\NoL + \NoV - (\NoL)(\NoV))}
\end{equation}$$
</p><p>
The implementation of the velvet NDF is presented in <a href="#listing_clothbrdf">listing&nbsp;17</a>, optimized to properly fit in half float formats and to avoid computing a costly cotangent, relying instead on trigonometric identities. Note that we removed the Fresnel component from this BRDF.
</p><pre class="listing tilde"><code><span class="line">float D_Ashikhmin(float roughness, float NoH) {</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-type">float</span> <span class="hljs-title">D_Ashikhmin</span><span class="hljs-params">(<span class="hljs-type">float</span> roughness, <span class="hljs-type">float</span> NoH)</span> </span>{</span>
<span class="line"> <span class="hljs-comment">// Ashikhmin 2007, &quot;Distribution-based BRDFs&quot;</span></span>
<span class="line"> float a<span class="hljs-number">2</span> = roughness * roughness;</span>
<span class="line"> float <span class="hljs-keyword">cos</span><span class="hljs-number">2</span>h = NoH * NoH;</span>
<span class="line"> float <span class="hljs-keyword">sin</span><span class="hljs-number">2</span>h = <span class="hljs-keyword">max</span>(<span class="hljs-number">1.0</span> - <span class="hljs-keyword">cos</span><span class="hljs-number">2</span>h, <span class="hljs-number">0.0078125</span>); <span class="hljs-comment">// 2^(-14/2), so sin2h^2 &gt; 0 in fp16</span></span>
<span class="line"> float <span class="hljs-keyword">sin</span><span class="hljs-number">4</span>h = <span class="hljs-keyword">sin</span><span class="hljs-number">2</span>h * <span class="hljs-keyword">sin</span><span class="hljs-number">2</span>h;</span>
<span class="line"> float cot<span class="hljs-number">2</span> = -<span class="hljs-keyword">cos</span><span class="hljs-number">2</span>h / (a<span class="hljs-number">2</span> * <span class="hljs-keyword">sin</span><span class="hljs-number">2</span>h);</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">1.0</span> / (PI * (<span class="hljs-number">4.0</span> * a<span class="hljs-number">2</span> + <span class="hljs-number">1.0</span>) * <span class="hljs-keyword">sin</span><span class="hljs-number">4</span>h) * (<span class="hljs-number">4.0</span> * exp(cot<span class="hljs-number">2</span>) + <span class="hljs-keyword">sin</span><span class="hljs-number">4</span>h);</span>
<span class="line"> <span class="hljs-type">float</span> a2 = roughness * roughness;</span>
<span class="line"> <span class="hljs-type">float</span> cos2h = NoH * NoH;</span>
<span class="line"> <span class="hljs-type">float</span> sin2h = <span class="hljs-built_in">max</span>(<span class="hljs-number">1.0</span> - cos2h, <span class="hljs-number">0.0078125</span>); <span class="hljs-comment">// 2^(-14/2), so sin2h^2 &gt; 0 in fp16</span></span>
<span class="line"> <span class="hljs-type">float</span> sin4h = sin2h * sin2h;</span>
<span class="line"> <span class="hljs-type">float</span> cot2 = -cos2h / (a2 * sin2h);</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">1.0</span> / (PI * (<span class="hljs-number">4.0</span> * a2 + <span class="hljs-number">1.0</span>) * sin4h) * (<span class="hljs-number">4.0</span> * <span class="hljs-built_in">exp</span>(cot2) + sin4h);</span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_clothbrdf">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;17:</b> Implementation of Ashikhmin's velvet NDF in GLSL</div></center>
<p>
<p>In [<a href="#citation-estevez17">Estevez17</a>] Estevez and Kulla propose a different NDF (called the “Charlie” sheen) that is based on an exponentiated sinusoidal instead of an inverted Gaussian. This NDF is appealing for several reasons: its parameterization feels more natural and intuitive, it provides a softer appearance and, as shown in equation (\ref{charlieNDF}), its implementation is simpler:</p>
@@ -1312,11 +1312,11 @@ D(m) = \frac{(2 + \frac{1}{\alpha}) sin(\theta)^{\frac{1}{\alpha}}}{2 \pi}
</p><p>
[<a href="#citation-estevez17">Estevez17</a>] also presents a new shadowing term that we omit here because of its cost. We instead rely on the visibility term from [<a href="#citation-neubelt13">Neubelt13</a>] (shown in equation \(\ref{clothSpecularBRDF}\) above).
The implementation of this NDF is presented in <a href="#listing_clothcharliebrdf">listing&nbsp;18</a>, optimized to properly fit in half float formats.
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-keyword">float</span> <span class="hljs-title">D_Charlie</span><span class="hljs-params">(<span class="hljs-keyword">float</span> roughness, <span class="hljs-keyword">float</span> NoH)</span> </span>{</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-type">float</span> <span class="hljs-title">D_Charlie</span><span class="hljs-params">(<span class="hljs-type">float</span> roughness, <span class="hljs-type">float</span> NoH)</span> </span>{</span>
<span class="line"> <span class="hljs-comment">// Estevez and Kulla 2017, &quot;Production Friendly Microfacet Sheen BRDF&quot;</span></span>
<span class="line"> <span class="hljs-keyword">float</span> invAlpha = <span class="hljs-number">1.0</span> / roughness;</span>
<span class="line"> <span class="hljs-keyword">float</span> cos2h = NoH * NoH;</span>
<span class="line"> <span class="hljs-keyword">float</span> sin2h = max(<span class="hljs-number">1.0</span> - cos2h, <span class="hljs-number">0.0078125</span>); <span class="hljs-comment">// 2^(-14/2), so sin2h^2 &gt; 0 in fp16</span></span>
<span class="line"> <span class="hljs-type">float</span> invAlpha = <span class="hljs-number">1.0</span> / roughness;</span>
<span class="line"> <span class="hljs-type">float</span> cos2h = NoH * NoH;</span>
<span class="line"> <span class="hljs-type">float</span> sin2h = <span class="hljs-built_in">max</span>(<span class="hljs-number">1.0</span> - cos2h, <span class="hljs-number">0.0078125</span>); <span class="hljs-comment">// 2^(-14/2), so sin2h^2 &gt; 0 in fp16</span></span>
<span class="line"> <span class="hljs-keyword">return</span> (<span class="hljs-number">2.0</span> + invAlpha) * <span class="hljs-built_in">pow</span>(sin2h, invAlpha * <span class="hljs-number">0.5</span>) / (<span class="hljs-number">2.0</span> * PI);</span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_clothcharliebrdf">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;18:</b> Implementation of the &ldquo;Charlie&rdquo; NDF in GLSL</div></center>
<a class="target" name="sheencolor">&nbsp;</a><a class="target" name="materialsystem/clothmodel/clothspecularbrdf/sheencolor">&nbsp;</a><a class="target" name="toc4.12.1.1">&nbsp;</a><h4 id="sheen-color"><a class="header" href="#sheen-color">Sheen color</a></h4>
@@ -1745,21 +1745,21 @@ The photometric attenuation function can be easily implemented in GLSL by adding
<span class="line">}</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_glslphotometricpunctuallight">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;22:</b> Implementation of attenuation from photometric profiles in GLSL</div></center>
<p>
<p>The light intensity is computed CPU-side (<a href="#listing_photometriclightintensity">listing 23</a>) and depends on whether the photometric profile is used as a mask.</p>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-keyword">float</span> multiplier;</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-type">float</span> multiplier;</span>
<span class="line"><span class="hljs-comment">// Photometric profile used as a mask</span></span>
<span class="line"><span class="hljs-keyword">if</span> (photometricLight.isMasked()) {</span>
<span class="line"><span class="hljs-keyword">if</span> (photometricLight.<span class="hljs-built_in">isMasked</span>()) {</span>
<span class="line"> <span class="hljs-comment">// The desired intensity is set by the artist</span></span>
<span class="line"> <span class="hljs-comment">// The integrated intensity comes from a Monte-Carlo</span></span>
<span class="line"> <span class="hljs-comment">// integration over the unit sphere around the luminaire</span></span>
<span class="line"> multiplier = photometricLight.getDesiredIntensity() /</span>
<span class="line"> photometricLight.getIntegratedIntensity();</span>
<span class="line"> multiplier = photometricLight.<span class="hljs-built_in">getDesiredIntensity</span>() /</span>
<span class="line"> photometricLight.<span class="hljs-built_in">getIntegratedIntensity</span>();</span>
<span class="line">} <span class="hljs-keyword">else</span> {</span>
<span class="line"> <span class="hljs-comment">// Multiplier provided for convenience, set to 1.0 by default</span></span>
<span class="line"> multiplier = photometricLight.getMultiplier();</span>
<span class="line"> multiplier = photometricLight.<span class="hljs-built_in">getMultiplier</span>();</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-comment">// The max intensity in cd comes from the IES profile</span></span>
<span class="line"><span class="hljs-keyword">float</span> lightIntensity = photometricLight.getMaxIntensity() * multiplier;</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_photometriclightintensity">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;23:</b> Computing the intensity of a photometric light on the CPU</div></center>
<span class="line"><span class="hljs-type">float</span> lightIntensity = photometricLight.<span class="hljs-built_in">getMaxIntensity</span>() * multiplier;</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_photometriclightintensity">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;23:</b> Computing the intensity of a photometric light on the CPU</div></center>
<p>
<div class="endnote"><a class="target" name="endnote-xarrowintensity">&nbsp;</a><sup>4</sup> The XArrow profile declares a luminous intensity of 1,750 lm but a Monte-Carlo integration shows an intensity of only 350 lm.
</div>
@@ -2058,19 +2058,19 @@ In practice only 4 or 9 coefficients (i.e.: 2 or 3 bands) are enough for \(\cosT
<center><div class="image" style=""><a href="../images/ibl/ibl_irradiance_sh2.png" target="_blank"><img class="markdeep" src="../images/ibl/ibl_irradiance_sh2.png" style="max-width:100%;" /></a><center><span class="imagecaption"><a class="target" name="figure_iblsh2">&nbsp;</a><b style="font-style:normal;">Figure&nbsp;52:</b> 2 bands (4 coefficients)</span></center></div></center>
</p><p>
In practice we pre-convolve \(\Lt\) with \(\cosTheta\) and pre-scale these coefficients by the basis scaling factors \(K_l^m\) so that the reconstruction code is as simple as possible in the shader:
</p><pre class="listing tilde"><code><span class="line">vec3 <span class="hljs-function"><span class="hljs-title">irradianceSH</span>(<span class="hljs-params">vec3 n</span>)</span> {</span>
<span class="line"> <span class="hljs-comment">// uniform vec3 sphericalHarmonics[9]</span></span>
<span class="line"> <span class="hljs-comment">// We can use only the first 2 bands for better performance</span></span>
<span class="line"> <span class="hljs-keyword">return</span></span>
<span class="line"> sphericalHarmonics[<span class="hljs-number">0</span>]</span>
<span class="line"> + sphericalHarmonics[<span class="hljs-number">1</span>] * (n.y)</span>
<span class="line"> + sphericalHarmonics[<span class="hljs-number">2</span>] * (n.z)</span>
<span class="line"> + sphericalHarmonics[<span class="hljs-number">3</span>] * (n.x)</span>
<span class="line"> + sphericalHarmonics[<span class="hljs-number">4</span>] * (n.y * n.x)</span>
<span class="line"> + sphericalHarmonics[<span class="hljs-number">5</span>] * (n.y * n.z)</span>
<span class="line"> + sphericalHarmonics[<span class="hljs-number">6</span>] * (<span class="hljs-number">3.0</span> * n.z * n.z - <span class="hljs-number">1.0</span>)</span>
<span class="line"> + sphericalHarmonics[<span class="hljs-number">7</span>] * (n.z * n.x)</span>
<span class="line"> + sphericalHarmonics[<span class="hljs-number">8</span>] * (n.x * n.x - n.y * n.y);</span>
</p><pre class="listing tilde"><code><span class="line">vec3 irradianceSH(vec3 n) {</span>
<span class="line"> // uniform vec3 sphericalHarmonics<span class="hljs-selector-attr">[9]</span></span>
<span class="line"> // We can <span class="hljs-selector-tag">use</span> only the first <span class="hljs-number">2</span> bands for better performance</span>
<span class="line"> return</span>
<span class="line"> sphericalHarmonics<span class="hljs-selector-attr">[0]</span></span>
<span class="line"> + sphericalHarmonics<span class="hljs-selector-attr">[1]</span> * (n<span class="hljs-selector-class">.y</span>)</span>
<span class="line"> + sphericalHarmonics<span class="hljs-selector-attr">[2]</span> * (n<span class="hljs-selector-class">.z</span>)</span>
<span class="line"> + sphericalHarmonics<span class="hljs-selector-attr">[3]</span> * (n<span class="hljs-selector-class">.x</span>)</span>
<span class="line"> + sphericalHarmonics<span class="hljs-selector-attr">[4]</span> * (n<span class="hljs-selector-class">.y</span> * n<span class="hljs-selector-class">.x</span>)</span>
<span class="line"> + sphericalHarmonics<span class="hljs-selector-attr">[5]</span> * (n<span class="hljs-selector-class">.y</span> * n<span class="hljs-selector-class">.z</span>)</span>
<span class="line"> + sphericalHarmonics<span class="hljs-selector-attr">[6]</span> * (<span class="hljs-number">3.0</span> * n<span class="hljs-selector-class">.z</span> * n<span class="hljs-selector-class">.z</span> - <span class="hljs-number">1.0</span>)</span>
<span class="line"> + sphericalHarmonics<span class="hljs-selector-attr">[7]</span> * (n<span class="hljs-selector-class">.z</span> * n<span class="hljs-selector-class">.x</span>)</span>
<span class="line"> + sphericalHarmonics<span class="hljs-selector-attr">[8]</span> * (n<span class="hljs-selector-class">.x</span> * n<span class="hljs-selector-class">.x</span> - n<span class="hljs-selector-class">.y</span> * n<span class="hljs-selector-class">.y</span>);</span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_irradiancesh">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;26:</b> GLSL code to reconstruct the irradiance from the pre-scaled SH</div></center>
<p>
<p>Note that with 2 bands, the computation above becomes a single (4 \times 4) matrix-by-vector multiply.</p>
@@ -2443,7 +2443,7 @@ LD(n, \alpha) &= \frac{\sum_i^N V(l_i, n,
$$
</p><p>
These two new \(DFG\) terms simply need to replace the ones used in the implementation shown in section <a href="#toc9.5">9.5</a>:
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-keyword">float</span> Fc = <span class="hljs-built_in">pow</span>(<span class="hljs-number">1</span> - VoH, <span class="hljs-number">5.0f</span>);</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-type">float</span> Fc = <span class="hljs-built_in">pow</span>(<span class="hljs-number">1</span> - VoH, <span class="hljs-number">5.0f</span>);</span>
<span class="line">r.x += Gv * Fc;</span>
<span class="line">r.y += Gv;</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_multiscatteriblpreintegration">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;29:</b> C++ implementation of the \(L_{DFG}\) term for multiscattering</div></center>
<p>
@@ -2507,11 +2507,11 @@ using an environment made of colored vertical stripes (skybox hidden).</span></c
<p>
<p>When sampling the IBL, the clear coat layer is calculated as a second specular lobe. This specular lobe is oriented along the view direction since we cannot reasonably integrate over the hemisphere. <a href="#listing_clearcoatibl">Listing 31</a> demonstrates this approximation in practice. It also shows the energy conservation step. It is important to note that this second specular lobe is computed exactly the same way as the main specular lobe, using the same DFG approximation.</p>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-comment">// clearCoat_NoV == shading_NoV if the clear coat layer doesn&#x27;t have its own normal map</span></span>
<span class="line"><span class="hljs-built_in">float</span> Fc = F_Schlick(<span class="hljs-number">0.04</span>, <span class="hljs-number">1.0</span>, clearCoat_NoV) * clearCoat;</span>
<span class="line"><span class="hljs-type">float</span> Fc = <span class="hljs-built_in">F_Schlick</span>(<span class="hljs-number">0.04</span>, <span class="hljs-number">1.0</span>, clearCoat_NoV) * clearCoat;</span>
<span class="line"><span class="hljs-comment">// base layer attenuation for energy compensation</span></span>
<span class="line">iblDiffuse *= <span class="hljs-number">1.0</span> - Fc;</span>
<span class="line">iblSpecular *= sq(<span class="hljs-number">1.0</span> - Fc);</span>
<span class="line">iblSpecular += specularIBL(r, clearCoatPerceptualRoughness) * Fc;</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_clearcoatibl">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;31:</b> GLSL implementation of the clear coat specular lobe for image-based lighting</div></center>
<span class="line">iblSpecular *= <span class="hljs-built_in">sq</span>(<span class="hljs-number">1.0</span> - Fc);</span>
<span class="line">iblSpecular += <span class="hljs-built_in">specularIBL</span>(r, clearCoatPerceptualRoughness) * Fc;</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_clearcoatibl">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;31:</b> GLSL implementation of the clear coat specular lobe for image-based lighting</div></center>
<a class="target" name="anisotropy">&nbsp;</a><a class="target" name="lighting/imagebasedlights/anisotropy">&nbsp;</a><a class="target" name="toc5.3.6">&nbsp;</a><h3 id="anisotropy"><a class="header" href="#anisotropy">Anisotropy </a></h3>
<p>
<p>[<a href="#citation-mcauley15">McAuley15</a>] describes a technique called “bent reflection vector”, based [<a href="#citation-revie12">Revie12</a>]. The bent reflection vector is a rough approximation of anisotropic lighting but the alternative is to use importance sampling. This approximation is sufficiently cheap to compute and provides good results, as shown in <a href="#figure_anisotropicibl1">figure 59</a> and <a href="#figure_anisotropicibl2">figure 60</a>.</p>
@@ -2550,17 +2550,17 @@ The DG term is generated using uniform sampling as recommended in [<a href="#cit
<center><div class="image" style=""><a href="../images/ibl/dfg_cloth.png" target="_blank"><img class="markdeep" src="../images/ibl/dfg_cloth.png" /></a><center><span class="imagecaption"><a class="target" name="figure_dfgclothlut">&nbsp;</a><b style="font-style:normal;">Figure&nbsp;62:</b> DFG LUT with a 3rd channel encoding the DG term of the cloth BRDF</span></center></div></center>
</p><p>
The remainder of the image-based lighting implementation follows the same steps as the implementation of regular lights, including the optional subsurface scattering term and its wrap diffuse component. Just as with the clear coat IBL implementation, we cannot integrate over the hemisphere and use the view direction as the dominant light direction to compute the wrap diffuse component.
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-built_in">float</span> diffuse = Fd_Lambert() * ambientOcclusion;</span>
<span class="line"><span class="hljs-meta">#<span class="hljs-meta-keyword">if</span> defined(SHADING_MODEL_CLOTH)</span></span>
<span class="line"><span class="hljs-meta">#<span class="hljs-meta-keyword">if</span> defined(MATERIAL_HAS_SUBSURFACE_COLOR)</span></span>
<span class="line">diffuse *= saturate((NoV + <span class="hljs-number">0.5</span>) / <span class="hljs-number">2.25</span>);</span>
<span class="line"><span class="hljs-meta">#<span class="hljs-meta-keyword">endif</span></span></span>
<span class="line"><span class="hljs-meta">#<span class="hljs-meta-keyword">endif</span></span></span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-type">float</span> diffuse = <span class="hljs-built_in">Fd_Lambert</span>() * ambientOcclusion;</span>
<span class="line"><span class="hljs-meta">#<span class="hljs-keyword">if</span> defined(SHADING_MODEL_CLOTH)</span></span>
<span class="line"><span class="hljs-meta">#<span class="hljs-keyword">if</span> defined(MATERIAL_HAS_SUBSURFACE_COLOR)</span></span>
<span class="line">diffuse *= <span class="hljs-built_in">saturate</span>((NoV + <span class="hljs-number">0.5</span>) / <span class="hljs-number">2.25</span>);</span>
<span class="line"><span class="hljs-meta">#<span class="hljs-keyword">endif</span></span></span>
<span class="line"><span class="hljs-meta">#<span class="hljs-keyword">endif</span></span></span>
<span class="line"></span>
<span class="line">vec3 indirectDiffuse = irradianceIBL(n) * diffuse;</span>
<span class="line"><span class="hljs-meta">#<span class="hljs-meta-keyword">if</span> defined(SHADING_MODEL_CLOTH) &amp;&amp; defined(MATERIAL_HAS_SUBSURFACE_COLOR)</span></span>
<span class="line">indirectDiffuse *= saturate(subsurfaceColor + NoV);</span>
<span class="line"><span class="hljs-meta">#<span class="hljs-meta-keyword">endif</span></span></span>
<span class="line">vec3 indirectDiffuse = <span class="hljs-built_in">irradianceIBL</span>(n) * diffuse;</span>
<span class="line"><span class="hljs-meta">#<span class="hljs-keyword">if</span> defined(SHADING_MODEL_CLOTH) &amp;&amp; defined(MATERIAL_HAS_SUBSURFACE_COLOR)</span></span>
<span class="line">indirectDiffuse *= <span class="hljs-built_in">saturate</span>(subsurfaceColor + NoV);</span>
<span class="line"><span class="hljs-meta">#<span class="hljs-keyword">endif</span></span></span>
<span class="line"></span>
<span class="line">vec3 ibl = diffuseColor * indirectDiffuse + indirectSpecular * specularColor;</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_clothapprox">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;34:</b> GLSL implementation of the DFG approximation for the cloth NDF</div></center>
<p>
@@ -2982,20 +2982,20 @@ L_{max} &= 2^{EV_{100}} \times 1.2
<span class="line"><span class="hljs-comment">// aperture in f-stops</span></span>
<span class="line"><span class="hljs-comment">// shutterSpeed in seconds</span></span>
<span class="line"><span class="hljs-comment">// sensitivity in ISO</span></span>
<span class="line"><span class="hljs-function"><span class="hljs-keyword">float</span> <span class="hljs-title">exposureSettings</span><span class="hljs-params">(<span class="hljs-keyword">float</span> aperture, <span class="hljs-keyword">float</span> shutterSpeed, <span class="hljs-keyword">float</span> sensitivity)</span> </span>{</span>
<span class="line"><span class="hljs-type">float</span> <span class="hljs-title function_">exposureSettings</span><span class="hljs-params">(<span class="hljs-type">float</span> aperture, <span class="hljs-type">float</span> shutterSpeed, <span class="hljs-type">float</span> sensitivity)</span> {</span>
<span class="line"> <span class="hljs-keyword">return</span> log2((aperture * aperture) / shutterSpeed * <span class="hljs-number">100.0</span> / sensitivity);</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-comment">// Computes the exposure normalization factor from</span></span>
<span class="line"><span class="hljs-comment">// the camera&#x27;s EV100</span></span>
<span class="line"><span class="hljs-function"><span class="hljs-keyword">float</span> <span class="hljs-title">exposure</span><span class="hljs-params">(<span class="hljs-keyword">float</span> ev100)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">1.0</span> / (<span class="hljs-built_in">pow</span>(<span class="hljs-number">2.0</span>, ev100) * <span class="hljs-number">1.2</span>);</span>
<span class="line"><span class="hljs-type">float</span> <span class="hljs-title function_">exposure</span><span class="hljs-params">(<span class="hljs-type">float</span> ev100)</span> {</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">1.0</span> / (pow(<span class="hljs-number">2.0</span>, ev100) * <span class="hljs-number">1.2</span>);</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-keyword">float</span> ev100 = exposureSettings(aperture, shutterSpeed, sensitivity);</span>
<span class="line"><span class="hljs-keyword">float</span> exposure = exposure(ev100);</span>
<span class="line"><span class="hljs-type">float</span> <span class="hljs-variable">ev100</span> <span class="hljs-operator">=</span> exposureSettings(aperture, shutterSpeed, sensitivity);</span>
<span class="line"><span class="hljs-type">float</span> <span class="hljs-variable">exposure</span> <span class="hljs-operator">=</span> exposure(ev100);</span>
<span class="line"></span>
<span class="line">vec4 color = evaluateLighting();</span>
<span class="line"><span class="hljs-type">vec4</span> <span class="hljs-variable">color</span> <span class="hljs-operator">=</span> evaluateLighting();</span>
<span class="line">color.rgb *= exposure;</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_fragmentexposure">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;42:</b> Implementation of exposure in GLSL</div></center>
<p>
<p>In practice the exposure factor can be pre-computed on the CPU to save shader instructions.</p>
@@ -3466,9 +3466,9 @@ Our implementation is presented in <a href="#listing_specularcolorimpl">listing&
<span class="line"><span class="hljs-comment">// Data source:</span></span>
<span class="line"><span class="hljs-comment">// http://cvrl.ioo.ucl.ac.uk/cmfs.htm</span></span>
<span class="line"><span class="hljs-comment">// http://cvrl.ioo.ucl.ac.uk/database/text/cmfs/ciexyz31.htm</span></span>
<span class="line"><span class="hljs-keyword">const</span> <span class="hljs-keyword">size_t</span> CIE_XYZ_START = <span class="hljs-number">360</span>;</span>
<span class="line"><span class="hljs-keyword">const</span> <span class="hljs-keyword">size_t</span> CIE_XYZ_COUNT = <span class="hljs-number">471</span>;</span>
<span class="line"><span class="hljs-keyword">const</span> float3 CIE_XYZ[CIE_XYZ_COUNT] = { ... };</span>
<span class="line"><span class="hljs-type">const</span> <span class="hljs-type">size_t</span> CIE_XYZ_START = <span class="hljs-number">360</span>;</span>
<span class="line"><span class="hljs-type">const</span> <span class="hljs-type">size_t</span> CIE_XYZ_COUNT = <span class="hljs-number">471</span>;</span>
<span class="line"><span class="hljs-type">const</span> float3 CIE_XYZ[CIE_XYZ_COUNT] = { ... };</span>
<span class="line"></span>
<span class="line"><span class="hljs-comment">// CIE Standard Illuminant D65 relative spectral power distribution,</span></span>
<span class="line"><span class="hljs-comment">// from 300nm to 830, at 5nm intervals</span></span>
@@ -3476,51 +3476,51 @@ Our implementation is presented in <a href="#listing_specularcolorimpl">listing&
<span class="line"><span class="hljs-comment">// Data source:</span></span>
<span class="line"><span class="hljs-comment">// https://en.wikipedia.org/wiki/Illuminant_D65</span></span>
<span class="line"><span class="hljs-comment">// https://cielab.xyz/pdf/CIE_sel_colorimetric_tables.xls</span></span>
<span class="line"><span class="hljs-keyword">const</span> <span class="hljs-keyword">size_t</span> CIE_D65_INTERVAL = <span class="hljs-number">5</span>;</span>
<span class="line"><span class="hljs-keyword">const</span> <span class="hljs-keyword">size_t</span> CIE_D65_START = <span class="hljs-number">300</span>;</span>
<span class="line"><span class="hljs-keyword">const</span> <span class="hljs-keyword">size_t</span> CIE_D65_END = <span class="hljs-number">830</span>;</span>
<span class="line"><span class="hljs-keyword">const</span> <span class="hljs-keyword">size_t</span> CIE_D65_COUNT = <span class="hljs-number">107</span>;</span>
<span class="line"><span class="hljs-keyword">const</span> <span class="hljs-keyword">float</span> CIE_D65[CIE_D65_COUNT] = { ... };</span>
<span class="line"><span class="hljs-type">const</span> <span class="hljs-type">size_t</span> CIE_D65_INTERVAL = <span class="hljs-number">5</span>;</span>
<span class="line"><span class="hljs-type">const</span> <span class="hljs-type">size_t</span> CIE_D65_START = <span class="hljs-number">300</span>;</span>
<span class="line"><span class="hljs-type">const</span> <span class="hljs-type">size_t</span> CIE_D65_END = <span class="hljs-number">830</span>;</span>
<span class="line"><span class="hljs-type">const</span> <span class="hljs-type">size_t</span> CIE_D65_COUNT = <span class="hljs-number">107</span>;</span>
<span class="line"><span class="hljs-type">const</span> <span class="hljs-type">float</span> CIE_D65[CIE_D65_COUNT] = { ... };</span>
<span class="line"></span>
<span class="line"><span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">Sample</span> {</span></span>
<span class="line"> <span class="hljs-keyword">float</span> w = <span class="hljs-number">0.0f</span>; <span class="hljs-comment">// wavelength</span></span>
<span class="line"> <span class="hljs-built_in">std</span>::<span class="hljs-built_in">complex</span>&lt;<span class="hljs-keyword">float</span>&gt; ior; <span class="hljs-comment">// complex IOR, n + ik</span></span>
<span class="line"><span class="hljs-keyword">struct</span> <span class="hljs-title class_">Sample</span> {</span>
<span class="line"> <span class="hljs-type">float</span> w = <span class="hljs-number">0.0f</span>; <span class="hljs-comment">// wavelength</span></span>
<span class="line"> std::complex&lt;<span class="hljs-type">float</span>&gt; ior; <span class="hljs-comment">// complex IOR, n + ik</span></span>
<span class="line">};</span>
<span class="line"></span>
<span class="line"><span class="hljs-function"><span class="hljs-keyword">static</span> <span class="hljs-keyword">float</span> <span class="hljs-title">illuminantD65</span><span class="hljs-params">(<span class="hljs-keyword">float</span> w)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">auto</span> i0 = <span class="hljs-keyword">size_t</span>((w - CIE_D65_START) / CIE_D65_INTERVAL);</span>
<span class="line"> uint2 indexBounds{i0, <span class="hljs-built_in">std</span>::min(i0 + <span class="hljs-number">1</span>, CIE_D65_END)};</span>
<span class="line"><span class="hljs-function"><span class="hljs-type">static</span> <span class="hljs-type">float</span> <span class="hljs-title">illuminantD65</span><span class="hljs-params">(<span class="hljs-type">float</span> w)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">auto</span> i0 = <span class="hljs-built_in">size_t</span>((w - CIE_D65_START) / CIE_D65_INTERVAL);</span>
<span class="line"> uint2 indexBounds{i0, std::<span class="hljs-built_in">min</span>(i0 + <span class="hljs-number">1</span>, CIE_D65_END)};</span>
<span class="line"></span>
<span class="line"> float2 wavelengthBounds = CIE_D65_START + float2{indexBounds} * CIE_D65_INTERVAL;</span>
<span class="line"> <span class="hljs-keyword">float</span> t = (w - wavelengthBounds.x) / (wavelengthBounds.y - wavelengthBounds.x);</span>
<span class="line"> <span class="hljs-keyword">return</span> lerp(CIE_D65[indexBounds.x], CIE_D65[indexBounds.y], t);</span>
<span class="line"> <span class="hljs-type">float</span> t = (w - wavelengthBounds.x) / (wavelengthBounds.y - wavelengthBounds.x);</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-built_in">lerp</span>(CIE_D65[indexBounds.x], CIE_D65[indexBounds.y], t);</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-comment">// For std::lower_bound</span></span>
<span class="line"><span class="hljs-keyword">bool</span> <span class="hljs-keyword">operator</span>&lt;(<span class="hljs-keyword">const</span> Sample&amp; lhs, <span class="hljs-keyword">const</span> Sample&amp; rhs) {</span>
<span class="line"><span class="hljs-type">bool</span> <span class="hljs-keyword">operator</span>&lt;(<span class="hljs-type">const</span> Sample&amp; lhs, <span class="hljs-type">const</span> Sample&amp; rhs) {</span>
<span class="line"> <span class="hljs-keyword">return</span> lhs.w &lt; rhs.w;</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-comment">// The wavelength w must be between 360nm and 830nm</span></span>
<span class="line"><span class="hljs-function"><span class="hljs-keyword">static</span> <span class="hljs-built_in">std</span>::<span class="hljs-built_in">complex</span>&lt;<span class="hljs-keyword">float</span>&gt; <span class="hljs-title">findSample</span><span class="hljs-params">(<span class="hljs-keyword">const</span> <span class="hljs-built_in">std</span>::<span class="hljs-built_in">vector</span>&lt;sample&gt;&amp; samples, <span class="hljs-keyword">float</span> w)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">auto</span> i1 = <span class="hljs-built_in">std</span>::lower_bound(</span>
<span class="line"> samples.begin(), samples.end(), Sample{w, <span class="hljs-number">0.0f</span> + <span class="hljs-number">0.0</span><span class="hljs-keyword">if</span>});</span>
<span class="line"><span class="hljs-function"><span class="hljs-type">static</span> std::complex&lt;<span class="hljs-type">float</span>&gt; <span class="hljs-title">findSample</span><span class="hljs-params">(<span class="hljs-type">const</span> std::vector&lt;sample&gt;&amp; samples, <span class="hljs-type">float</span> w)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">auto</span> i1 = std::<span class="hljs-built_in">lower_bound</span>(</span>
<span class="line"> samples.<span class="hljs-built_in">begin</span>(), samples.<span class="hljs-built_in">end</span>(), Sample{w, <span class="hljs-number">0.0f</span> + <span class="hljs-number">0.0</span><span class="hljs-keyword">if</span>});</span>
<span class="line"> <span class="hljs-keyword">auto</span> i0 = i1 - <span class="hljs-number">1</span>;</span>
<span class="line"></span>
<span class="line"> <span class="hljs-comment">// Interpolate the complex IORs</span></span>
<span class="line"> <span class="hljs-keyword">float</span> t = (w - i0-&gt;w) / (i1-&gt;w - i0-&gt;w);</span>
<span class="line"> <span class="hljs-keyword">float</span> n = lerp(i0-&gt;ior.real(), i1-&gt;ior.real(), t);</span>
<span class="line"> <span class="hljs-keyword">float</span> k = lerp(i0-&gt;ior.imag(), i1-&gt;ior.imag(), t);</span>
<span class="line"> <span class="hljs-type">float</span> t = (w - i0-&gt;w) / (i1-&gt;w - i0-&gt;w);</span>
<span class="line"> <span class="hljs-type">float</span> n = <span class="hljs-built_in">lerp</span>(i0-&gt;ior.<span class="hljs-built_in">real</span>(), i1-&gt;ior.<span class="hljs-built_in">real</span>(), t);</span>
<span class="line"> <span class="hljs-type">float</span> k = <span class="hljs-built_in">lerp</span>(i0-&gt;ior.<span class="hljs-built_in">imag</span>(), i1-&gt;ior.<span class="hljs-built_in">imag</span>(), t);</span>
<span class="line"> <span class="hljs-keyword">return</span> { n, k };</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-function"><span class="hljs-keyword">static</span> <span class="hljs-keyword">float</span> <span class="hljs-title">fresnel</span><span class="hljs-params">(<span class="hljs-keyword">const</span> <span class="hljs-built_in">std</span>::<span class="hljs-built_in">complex</span>&lt;<span class="hljs-keyword">float</span>&gt;&amp; sample)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">return</span> (((sample - (<span class="hljs-number">1.0f</span> + <span class="hljs-number">0</span><span class="hljs-keyword">if</span>)) * (<span class="hljs-built_in">std</span>::conj(sample) - (<span class="hljs-number">1.0f</span> + <span class="hljs-number">0</span><span class="hljs-keyword">if</span>))) /</span>
<span class="line"> ((sample + (<span class="hljs-number">1.0f</span> + <span class="hljs-number">0</span><span class="hljs-keyword">if</span>)) * (<span class="hljs-built_in">std</span>::conj(sample) + (<span class="hljs-number">1.0f</span> + <span class="hljs-number">0</span><span class="hljs-keyword">if</span>)))).real();</span>
<span class="line"><span class="hljs-function"><span class="hljs-type">static</span> <span class="hljs-type">float</span> <span class="hljs-title">fresnel</span><span class="hljs-params">(<span class="hljs-type">const</span> std::complex&lt;<span class="hljs-type">float</span>&gt;&amp; sample)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">return</span> (((sample - (<span class="hljs-number">1.0f</span> + <span class="hljs-number">0</span><span class="hljs-keyword">if</span>)) * (std::<span class="hljs-built_in">conj</span>(sample) - (<span class="hljs-number">1.0f</span> + <span class="hljs-number">0</span><span class="hljs-keyword">if</span>))) /</span>
<span class="line"> ((sample + (<span class="hljs-number">1.0f</span> + <span class="hljs-number">0</span><span class="hljs-keyword">if</span>)) * (std::<span class="hljs-built_in">conj</span>(sample) + (<span class="hljs-number">1.0f</span> + <span class="hljs-number">0</span><span class="hljs-keyword">if</span>)))).<span class="hljs-built_in">real</span>();</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-function"><span class="hljs-keyword">static</span> float3 <span class="hljs-title">XYZ_to_sRGB</span><span class="hljs-params">(<span class="hljs-keyword">const</span> float3&amp; v)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">const</span> mat3f XYZ_sRGB{</span>
<span class="line"><span class="hljs-function"><span class="hljs-type">static</span> float3 <span class="hljs-title">XYZ_to_sRGB</span><span class="hljs-params">(<span class="hljs-type">const</span> float3&amp; v)</span> </span>{</span>
<span class="line"> <span class="hljs-type">const</span> mat3f XYZ_sRGB{</span>
<span class="line"> <span class="hljs-number">3.2404542f</span>, <span class="hljs-number">-0.9692660f</span>, <span class="hljs-number">0.0556434f</span>,</span>
<span class="line"> <span class="hljs-number">-1.5371385f</span>, <span class="hljs-number">1.8760108f</span>, <span class="hljs-number">-0.2040259f</span>,</span>
<span class="line"> <span class="hljs-number">-0.4985314f</span>, <span class="hljs-number">0.0415560f</span>, <span class="hljs-number">1.0572252f</span></span>
@@ -3529,21 +3529,21 @@ Our implementation is presented in <a href="#listing_specularcolorimpl">listing&
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-comment">// Outputs a linear sRGB color</span></span>
<span class="line"><span class="hljs-function"><span class="hljs-keyword">static</span> float3 <span class="hljs-title">computeColor</span><span class="hljs-params">(<span class="hljs-keyword">const</span> <span class="hljs-built_in">std</span>::<span class="hljs-built_in">vector</span>&lt;sample&gt;&amp; samples)</span> </span>{</span>
<span class="line"><span class="hljs-function"><span class="hljs-type">static</span> float3 <span class="hljs-title">computeColor</span><span class="hljs-params">(<span class="hljs-type">const</span> std::vector&lt;sample&gt;&amp; samples)</span> </span>{</span>
<span class="line"> float3 xyz{<span class="hljs-number">0.0f</span>};</span>
<span class="line"> <span class="hljs-keyword">float</span> y = <span class="hljs-number">0.0f</span>;</span>
<span class="line"> <span class="hljs-type">float</span> y = <span class="hljs-number">0.0f</span>;</span>
<span class="line"></span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-keyword">size_t</span> i = <span class="hljs-number">0</span>; i &lt; CIE_XYZ_COUNT; i++) {</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">size_t</span> i = <span class="hljs-number">0</span>; i &lt; CIE_XYZ_COUNT; i++) {</span>
<span class="line"> <span class="hljs-comment">// Current wavelength</span></span>
<span class="line"> <span class="hljs-keyword">float</span> w = CIE_XYZ_START + i;</span>
<span class="line"> <span class="hljs-type">float</span> w = CIE_XYZ_START + i;</span>
<span class="line"></span>
<span class="line"> <span class="hljs-comment">// Find most appropriate CIE XYZ sample for the wavelength</span></span>
<span class="line"> <span class="hljs-keyword">auto</span> sample = findSample(samples, w);</span>
<span class="line"> <span class="hljs-keyword">auto</span> sample = <span class="hljs-built_in">findSample</span>(samples, w);</span>
<span class="line"> <span class="hljs-comment">// Compute Fresnel reflectance at normal incidence</span></span>
<span class="line"> <span class="hljs-keyword">float</span> f0 = fresnel(sample);</span>
<span class="line"> <span class="hljs-type">float</span> f0 = <span class="hljs-built_in">fresnel</span>(sample);</span>
<span class="line"></span>
<span class="line"> <span class="hljs-comment">// We need to multiply by the spectral power distribution of the illuminant</span></span>
<span class="line"> <span class="hljs-keyword">float</span> d65 = illuminantD65(w);</span>
<span class="line"> <span class="hljs-type">float</span> d65 = <span class="hljs-built_in">illuminantD65</span>(w);</span>
<span class="line"></span>
<span class="line"> xyz += f0 * CIE_XYZ[i] * d65;</span>
<span class="line"> y += CIE_XYZ[i].y * d65;</span>
@@ -3552,10 +3552,10 @@ Our implementation is presented in <a href="#listing_specularcolorimpl">listing&
<span class="line"> <span class="hljs-comment">// Normalize so that 100% reflectance at every wavelength yields Y=1</span></span>
<span class="line"> xyz /= y;</span>
<span class="line"></span>
<span class="line"> float3 linear = XYZ_to_sRGB(xyz);</span>
<span class="line"> float3 linear = <span class="hljs-built_in">XYZ_to_sRGB</span>(xyz);</span>
<span class="line"></span>
<span class="line"> <span class="hljs-comment">// Normalize out-of-gamut values</span></span>
<span class="line"> <span class="hljs-keyword">if</span> (any(greaterThan(linear, float3{<span class="hljs-number">1.0f</span>}))) linear *= <span class="hljs-number">1.0f</span> / max(linear);</span>
<span class="line"> <span class="hljs-keyword">if</span> (<span class="hljs-built_in">any</span>(<span class="hljs-built_in">greaterThan</span>(linear, float3{<span class="hljs-number">1.0f</span>}))) linear *= <span class="hljs-number">1.0f</span> / <span class="hljs-built_in">max</span>(linear);</span>
<span class="line"></span>
<span class="line"> <span class="hljs-keyword">return</span> linear;</span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde"><a class="target" name="listing_specularcolorimpl">&nbsp;</a><b style="font-style:normal;">Listing&nbsp;46:</b> C++ implementation to compute the base color of a metallic surface from spectral data</div></center>
@@ -3735,47 +3735,47 @@ l &= \{ cos\phi sin\theta,sin\phi sin\theta,cos\theta \}
<pre class="listing tilde"><code><span class="line">vec2f hammersley(uint i, <span class="hljs-built_in">float</span> numSamples) {</span>
<span class="line"> uint bits = i;</span>
<span class="line"> bits = (bits &lt;&lt; <span class="hljs-string">16) | (bits &gt;&gt; 16</span>);</span>
<span class="line"> bits = ((bits &amp; 0x55555555) &lt;&lt; <span class="hljs-string">1) | ((bits &amp; 0xAAAAAAAA) &gt;&gt; 1</span>);</span>
<span class="line"> bits = ((bits &amp; 0x33333333) &lt;&lt; <span class="hljs-string">2) | ((bits &amp; 0xCCCCCCCC) &gt;&gt; 2</span>);</span>
<span class="line"> bits = ((bits &amp; 0x0F0F0F0F) &lt;&lt; <span class="hljs-string">4) | ((bits &amp; 0xF0F0F0F0) &gt;&gt; 4</span>);</span>
<span class="line"> bits = ((bits &amp; 0x00FF00FF) &lt;&lt; <span class="hljs-string">8) | ((bits &amp; 0xFF00FF00) &gt;&gt; 8</span>);</span>
<span class="line"> <span class="hljs-built_in">return</span> vec2f(i / numSamples, bits / exp2(32));</span>
<span class="line"> bits = ((bits &amp; <span class="hljs-number">0</span>x55555555) &lt;&lt; <span class="hljs-number">1</span>) | ((bits &amp; <span class="hljs-number">0</span>xAAAAAAAA) &gt;&gt; <span class="hljs-number">1</span>);</span>
<span class="line"> bits = ((bits &amp; <span class="hljs-number">0</span>x33333333) &lt;&lt; <span class="hljs-number">2</span>) | ((bits &amp; <span class="hljs-number">0</span>xCCCCCCCC) &gt;&gt; <span class="hljs-number">2</span>);</span>
<span class="line"> bits = ((bits &amp; <span class="hljs-number">0</span>x0F0F0F0F) &lt;&lt; <span class="hljs-number">4</span>) | ((bits &amp; <span class="hljs-number">0</span>xF0F0F0F0) &gt;&gt; <span class="hljs-number">4</span>);</span>
<span class="line"> bits = ((bits &amp; <span class="hljs-number">0</span>x00FF00FF) &lt;&lt; <span class="hljs-number">8</span>) | ((bits &amp; <span class="hljs-number">0</span>xFF00FF00) &gt;&gt; <span class="hljs-number">8</span>);</span>
<span class="line"> return vec2f(i / numSamples, bits / exp2(<span class="hljs-number">32</span>));</span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde">C++ implementation of a Hammersley sequence generator</div></center>
<a class="target" name="precomputinglforimage-basedlighting">&nbsp;</a><a class="target" name="annex/precomputinglforimage-basedlighting">&nbsp;</a><a class="target" name="toc9.5">&nbsp;</a><h2 id="precomputing-l-for-image-based-lighting"><a class="header" href="#precomputing-l-for-image-based-lighting">Precomputing L for image-based lighting</a></h2>
<p>
<p>The term ( L_{DFG} ) is only dependent on ( \NoV ). Below, the normal is arbitrarily set to ( n=\left[0, 0, 1\right] ) and (v) is chosen to satisfy ( \NoV ). The vector ( h_i ) is the ( D_{GGX}(\alpha) ) important direction sample (i).</p>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-type">float</span> GDFG(<span class="hljs-type">float</span> NoV, <span class="hljs-type">float</span> NoL, <span class="hljs-type">float</span> a) {</span>
<span class="line"> <span class="hljs-type">float</span> a2 = a * a;</span>
<span class="line"> <span class="hljs-type">float</span> GGXL = NoV * <span class="hljs-built_in">sqrt</span>((-NoL * a2 + NoL) * NoL + a2);</span>
<span class="line"> <span class="hljs-type">float</span> GGXV = NoL * <span class="hljs-built_in">sqrt</span>((-NoV * a2 + NoV) * NoV + a2);</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-type">float</span> <span class="hljs-title function_">GDFG</span><span class="hljs-params">(<span class="hljs-type">float</span> NoV, <span class="hljs-type">float</span> NoL, <span class="hljs-type">float</span> a)</span> {</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">a2</span> <span class="hljs-operator">=</span> a * a;</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">GGXL</span> <span class="hljs-operator">=</span> NoV * sqrt((-NoL * a2 + NoL) * NoL + a2);</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">GGXV</span> <span class="hljs-operator">=</span> NoL * sqrt((-NoV * a2 + NoV) * NoV + a2);</span>
<span class="line"> <span class="hljs-keyword">return</span> (<span class="hljs-number">2</span> * NoL) / (GGXV + GGXL);</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line">float2 DFG(<span class="hljs-type">float</span> NoV, <span class="hljs-type">float</span> a) {</span>
<span class="line">float2 <span class="hljs-title function_">DFG</span><span class="hljs-params">(<span class="hljs-type">float</span> NoV, <span class="hljs-type">float</span> a)</span> {</span>
<span class="line"> float3 V;</span>
<span class="line"> V.x = <span class="hljs-built_in">sqrt</span>(<span class="hljs-number">1.0</span>f - NoV*NoV);</span>
<span class="line"> V.y = <span class="hljs-number">0.0</span>f;</span>
<span class="line"> V.x = sqrt(<span class="hljs-number">1.0f</span> - NoV*NoV);</span>
<span class="line"> V.y = <span class="hljs-number">0.0f</span>;</span>
<span class="line"> V.z = NoV;</span>
<span class="line"></span>
<span class="line"> float2 r = <span class="hljs-number">0.0</span>f;</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">uint</span> i = <span class="hljs-number">0</span>; i &lt; sampleCount; i++) {</span>
<span class="line"> float2 Xi = hammersley(i, sampleCount);</span>
<span class="line"> float3 H = importanceSampleGGX(Xi, a, N);</span>
<span class="line"> float3 L = <span class="hljs-number">2.0</span>f * <span class="hljs-built_in">dot</span>(V, H) * H - V;</span>
<span class="line"> <span class="hljs-type">float2</span> <span class="hljs-variable">r</span> <span class="hljs-operator">=</span> <span class="hljs-number">0.0f</span>;</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">uint</span> <span class="hljs-variable">i</span> <span class="hljs-operator">=</span> <span class="hljs-number">0</span>; i &lt; sampleCount; i++) {</span>
<span class="line"> <span class="hljs-type">float2</span> <span class="hljs-variable">Xi</span> <span class="hljs-operator">=</span> hammersley(i, sampleCount);</span>
<span class="line"> <span class="hljs-type">float3</span> <span class="hljs-variable">H</span> <span class="hljs-operator">=</span> importanceSampleGGX(Xi, a, N);</span>
<span class="line"> <span class="hljs-type">float3</span> <span class="hljs-variable">L</span> <span class="hljs-operator">=</span> <span class="hljs-number">2.0f</span> * dot(V, H) * H - V;</span>
<span class="line"></span>
<span class="line"> <span class="hljs-type">float</span> VoH = saturate(<span class="hljs-built_in">dot</span>(V, H));</span>
<span class="line"> <span class="hljs-type">float</span> NoL = saturate(L.z);</span>
<span class="line"> <span class="hljs-type">float</span> NoH = saturate(H.z);</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">VoH</span> <span class="hljs-operator">=</span> saturate(dot(V, H));</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">NoL</span> <span class="hljs-operator">=</span> saturate(L.z);</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">NoH</span> <span class="hljs-operator">=</span> saturate(H.z);</span>
<span class="line"></span>
<span class="line"> <span class="hljs-keyword">if</span> (NoL &gt; <span class="hljs-number">0.0</span>f) {</span>
<span class="line"> <span class="hljs-type">float</span> G = GDFG(NoV, NoL, a);</span>
<span class="line"> <span class="hljs-type">float</span> Gv = G * VoH / NoH;</span>
<span class="line"> <span class="hljs-type">float</span> Fc = <span class="hljs-built_in">pow</span>(<span class="hljs-number">1</span> - VoH, <span class="hljs-number">5.0</span>f);</span>
<span class="line"> <span class="hljs-keyword">if</span> (NoL &gt; <span class="hljs-number">0.0f</span>) {</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">G</span> <span class="hljs-operator">=</span> GDFG(NoV, NoL, a);</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">Gv</span> <span class="hljs-operator">=</span> G * VoH / NoH;</span>
<span class="line"> <span class="hljs-type">float</span> <span class="hljs-variable">Fc</span> <span class="hljs-operator">=</span> pow(<span class="hljs-number">1</span> - VoH, <span class="hljs-number">5.0f</span>);</span>
<span class="line"> r.x += Gv * (<span class="hljs-number">1</span> - Fc);</span>
<span class="line"> r.y += Gv * Fc;</span>
<span class="line"> }</span>
<span class="line"> }</span>
<span class="line"> <span class="hljs-keyword">return</span> r * (<span class="hljs-number">1.0</span>f / sampleCount);</span>
<span class="line"> <span class="hljs-keyword">return</span> r * (<span class="hljs-number">1.0f</span> / sampleCount);</span>
<span class="line">}</span></code></pre><center><div class="listingcaption tilde">C++ implementation of the \( L_{DFG} \) term</div></center>
<a class="target" name="sphericalharmonics">&nbsp;</a><a class="target" name="annex/sphericalharmonics">&nbsp;</a><a class="target" name="toc9.6">&nbsp;</a><h2 id="spherical-harmonics"><a class="header" href="#spherical-harmonics">Spherical Harmonics</a></h2>
<p>
@@ -3851,56 +3851,56 @@ sin(m \phi + \phi) &= sin(m \phi) cos(\phi) + cos(m \phi) sin(\phi) \Leftrightar
\end{align*}$$
</p><p>
<a href="#listing_nonnormalizedshbasis">Listing&nbsp;47</a> shows the C++ code to compute the non-normalized SH basis \(\frac{y^m_l(s)}{\sqrt{2} K^m_l}\):
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-keyword">static</span> <span class="hljs-keyword">inline</span> <span class="hljs-keyword">size_t</span> <span class="hljs-title">SHindex</span><span class="hljs-params">(<span class="hljs-keyword">ssize_t</span> m, <span class="hljs-keyword">size_t</span> l)</span> </span>{</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-type">static</span> <span class="hljs-keyword">inline</span> <span class="hljs-type">size_t</span> <span class="hljs-title">SHindex</span><span class="hljs-params">(<span class="hljs-type">ssize_t</span> m, <span class="hljs-type">size_t</span> l)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">return</span> l * (l + <span class="hljs-number">1</span>) + m;</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">computeShBasis</span><span class="hljs-params">(</span>
<span class="line"> <span class="hljs-keyword">double</span>* <span class="hljs-keyword">const</span> SHb,</span>
<span class="line"> <span class="hljs-keyword">size_t</span> numBands,</span>
<span class="line"> <span class="hljs-keyword">const</span> vec3&amp; s)</span></span>
<span class="line"><span class="hljs-function"><span class="hljs-type">void</span> <span class="hljs-title">computeShBasis</span><span class="hljs-params">(</span>
<span class="line"> <span class="hljs-type">double</span>* <span class="hljs-type">const</span> SHb,</span>
<span class="line"> <span class="hljs-type">size_t</span> numBands,</span>
<span class="line"> <span class="hljs-type">const</span> vec3&amp; s)</span></span>
<span class="line"></span>{</span>
<span class="line"> <span class="hljs-comment">// handle m=0 separately, since it produces only one coefficient</span></span>
<span class="line"> <span class="hljs-keyword">double</span> Pml_2 = <span class="hljs-number">0</span>;</span>
<span class="line"> <span class="hljs-keyword">double</span> Pml_1 = <span class="hljs-number">1</span>;</span>
<span class="line"> <span class="hljs-type">double</span> Pml_2 = <span class="hljs-number">0</span>;</span>
<span class="line"> <span class="hljs-type">double</span> Pml_1 = <span class="hljs-number">1</span>;</span>
<span class="line"> SHb[<span class="hljs-number">0</span>] = Pml_1;</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-keyword">ssize_t</span> l = <span class="hljs-number">1</span>; l &lt; numBands; l++) {</span>
<span class="line"> <span class="hljs-keyword">double</span> Pml = ((<span class="hljs-number">2</span> * l - <span class="hljs-number">1</span>) * Pml_1 * s.z - (l - <span class="hljs-number">1</span>) * Pml_2) / l;</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">ssize_t</span> l = <span class="hljs-number">1</span>; l &lt; numBands; l++) {</span>
<span class="line"> <span class="hljs-type">double</span> Pml = ((<span class="hljs-number">2</span> * l - <span class="hljs-number">1</span>) * Pml_1 * s.z - (l - <span class="hljs-number">1</span>) * Pml_2) / l;</span>
<span class="line"> Pml_2 = Pml_1;</span>
<span class="line"> Pml_1 = Pml;</span>
<span class="line"> SHb[SHindex(<span class="hljs-number">0</span>, l)] = Pml;</span>
<span class="line"> SHb[<span class="hljs-built_in">SHindex</span>(<span class="hljs-number">0</span>, l)] = Pml;</span>
<span class="line"> }</span>
<span class="line"> <span class="hljs-keyword">double</span> Pmm = <span class="hljs-number">1</span>;</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-keyword">ssize_t</span> m = <span class="hljs-number">1</span>; m &lt; numBands ; m++) {</span>
<span class="line"> <span class="hljs-type">double</span> Pmm = <span class="hljs-number">1</span>;</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">ssize_t</span> m = <span class="hljs-number">1</span>; m &lt; numBands ; m++) {</span>
<span class="line"> Pmm = (<span class="hljs-number">1</span> - <span class="hljs-number">2</span> * m) * Pmm;</span>
<span class="line"> <span class="hljs-keyword">double</span> Pml_2 = Pmm;</span>
<span class="line"> <span class="hljs-keyword">double</span> Pml_1 = (<span class="hljs-number">2</span> * m + <span class="hljs-number">1</span>)*Pmm*s.z;</span>
<span class="line"> <span class="hljs-type">double</span> Pml_2 = Pmm;</span>
<span class="line"> <span class="hljs-type">double</span> Pml_1 = (<span class="hljs-number">2</span> * m + <span class="hljs-number">1</span>)*Pmm*s.z;</span>
<span class="line"> <span class="hljs-comment">// l == m</span></span>
<span class="line"> SHb[SHindex(-m, m)] = Pml_2;</span>
<span class="line"> SHb[SHindex( m, m)] = Pml_2;</span>
<span class="line"> SHb[<span class="hljs-built_in">SHindex</span>(-m, m)] = Pml_2;</span>
<span class="line"> SHb[<span class="hljs-built_in">SHindex</span>( m, m)] = Pml_2;</span>
<span class="line"> <span class="hljs-keyword">if</span> (m + <span class="hljs-number">1</span> &lt; numBands) {</span>
<span class="line"> <span class="hljs-comment">// l == m+1</span></span>
<span class="line"> SHb[SHindex(-m, m + <span class="hljs-number">1</span>)] = Pml_1;</span>
<span class="line"> SHb[SHindex( m, m + <span class="hljs-number">1</span>)] = Pml_1;</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-keyword">ssize_t</span> l = m + <span class="hljs-number">2</span>; l &lt; numBands; l++) {</span>
<span class="line"> <span class="hljs-keyword">double</span> Pml = ((<span class="hljs-number">2</span> * l - <span class="hljs-number">1</span>) * Pml_1 * s.z - (l + m - <span class="hljs-number">1</span>) * Pml_2)</span>
<span class="line"> SHb[<span class="hljs-built_in">SHindex</span>(-m, m + <span class="hljs-number">1</span>)] = Pml_1;</span>
<span class="line"> SHb[<span class="hljs-built_in">SHindex</span>( m, m + <span class="hljs-number">1</span>)] = Pml_1;</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">ssize_t</span> l = m + <span class="hljs-number">2</span>; l &lt; numBands; l++) {</span>
<span class="line"> <span class="hljs-type">double</span> Pml = ((<span class="hljs-number">2</span> * l - <span class="hljs-number">1</span>) * Pml_1 * s.z - (l + m - <span class="hljs-number">1</span>) * Pml_2)</span>
<span class="line"> / (l - m);</span>
<span class="line"> Pml_2 = Pml_1;</span>
<span class="line"> Pml_1 = Pml;</span>
<span class="line"> SHb[SHindex(-m, l)] = Pml;</span>
<span class="line"> SHb[SHindex( m, l)] = Pml;</span>
<span class="line"> SHb[<span class="hljs-built_in">SHindex</span>(-m, l)] = Pml;</span>
<span class="line"> SHb[<span class="hljs-built_in">SHindex</span>( m, l)] = Pml;</span>
<span class="line"> }</span>
<span class="line"> }</span>
<span class="line"> }</span>
<span class="line"> <span class="hljs-keyword">double</span> Cm = s.x;</span>
<span class="line"> <span class="hljs-keyword">double</span> Sm = s.y;</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-keyword">ssize_t</span> m = <span class="hljs-number">1</span>; m &lt;= numBands ; m++) {</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-keyword">ssize_t</span> l = m; l &lt; numBands ; l++) {</span>
<span class="line"> SHb[SHindex(-m, l)] *= Sm;</span>
<span class="line"> SHb[SHindex( m, l)] *= Cm;</span>
<span class="line"> <span class="hljs-type">double</span> Cm = s.x;</span>
<span class="line"> <span class="hljs-type">double</span> Sm = s.y;</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">ssize_t</span> m = <span class="hljs-number">1</span>; m &lt;= numBands ; m++) {</span>
<span class="line"> <span class="hljs-keyword">for</span> (<span class="hljs-type">ssize_t</span> l = m; l &lt; numBands ; l++) {</span>
<span class="line"> SHb[<span class="hljs-built_in">SHindex</span>(-m, l)] *= Sm;</span>
<span class="line"> SHb[<span class="hljs-built_in">SHindex</span>( m, l)] *= Cm;</span>
<span class="line"> }</span>
<span class="line"> <span class="hljs-keyword">double</span> Cm1 = Cm * s.x - Sm * s.y;</span>
<span class="line"> <span class="hljs-keyword">double</span> Sm1 = Sm * s.x + Cm * s.y;</span>
<span class="line"> <span class="hljs-type">double</span> Cm1 = Cm * s.x - Sm * s.y;</span>
<span class="line"> <span class="hljs-type">double</span> Sm1 = Sm * s.x + Cm * s.y;</span>
<span class="line"> Cm = Cm1;</span>
<span class="line"> Sm = Sm1;</span>
<span class="line"> }</span>
@@ -3979,10 +3979,10 @@ $$\begin{equation}
\end{equation}$$
</p><p>
Here is the C++ code to compute \(\hat{C}_l\):
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-keyword">static</span> <span class="hljs-keyword">double</span> <span class="hljs-title">factorial</span><span class="hljs-params">(<span class="hljs-keyword">size_t</span> n, <span class="hljs-keyword">size_t</span> d = <span class="hljs-number">1</span>)</span></span>;</span>
</p><pre class="listing tilde"><code><span class="line"><span class="hljs-function"><span class="hljs-type">static</span> <span class="hljs-type">double</span> <span class="hljs-title">factorial</span><span class="hljs-params">(<span class="hljs-type">size_t</span> n, <span class="hljs-type">size_t</span> d = <span class="hljs-number">1</span>)</span></span>;</span>
<span class="line"></span>
<span class="line"><span class="hljs-comment">// &lt; cos(theta) &gt; SH coefficients pre-multiplied by 1 / K(0,l)</span></span>
<span class="line"><span class="hljs-function"><span class="hljs-keyword">double</span> <span class="hljs-title">computeTruncatedCosSh</span><span class="hljs-params">(<span class="hljs-keyword">size_t</span> l)</span> </span>{</span>
<span class="line"><span class="hljs-function"><span class="hljs-type">double</span> <span class="hljs-title">computeTruncatedCosSh</span><span class="hljs-params">(<span class="hljs-type">size_t</span> l)</span> </span>{</span>
<span class="line"> <span class="hljs-keyword">if</span> (l == <span class="hljs-number">0</span>) {</span>
<span class="line"> <span class="hljs-keyword">return</span> M_PI;</span>
<span class="line"> } <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (l == <span class="hljs-number">1</span>) {</span>
@@ -3990,17 +3990,17 @@ Here is the C++ code to compute \(\hat{C}_l\):
<span class="line"> } <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (l &amp; <span class="hljs-number">1</span>) {</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;</span>
<span class="line"> }</span>
<span class="line"> <span class="hljs-keyword">const</span> <span class="hljs-keyword">size_t</span> l_2 = l / <span class="hljs-number">2</span>;</span>
<span class="line"> <span class="hljs-keyword">double</span> A0 = ((l_2 &amp; <span class="hljs-number">1</span>) ? <span class="hljs-number">1.0</span> : <span class="hljs-number">-1.0</span>) / ((l + <span class="hljs-number">2</span>) * (l - <span class="hljs-number">1</span>));</span>
<span class="line"> <span class="hljs-keyword">double</span> A1 = factorial(l, l_2) / (factorial(l_2) * (<span class="hljs-number">1</span> &lt;&lt; l));</span>
<span class="line"> <span class="hljs-type">const</span> <span class="hljs-type">size_t</span> l_2 = l / <span class="hljs-number">2</span>;</span>
<span class="line"> <span class="hljs-type">double</span> A0 = ((l_2 &amp; <span class="hljs-number">1</span>) ? <span class="hljs-number">1.0</span> : <span class="hljs-number">-1.0</span>) / ((l + <span class="hljs-number">2</span>) * (l - <span class="hljs-number">1</span>));</span>
<span class="line"> <span class="hljs-type">double</span> A1 = <span class="hljs-built_in">factorial</span>(l, l_2) / (<span class="hljs-built_in">factorial</span>(l_2) * (<span class="hljs-number">1</span> &lt;&lt; l));</span>
<span class="line"> <span class="hljs-keyword">return</span> <span class="hljs-number">2</span> * M_PI * A0 * A1;</span>
<span class="line">}</span>
<span class="line"></span>
<span class="line"><span class="hljs-comment">// returns n! / d!</span></span>
<span class="line"><span class="hljs-function"><span class="hljs-keyword">double</span> <span class="hljs-title">factorial</span><span class="hljs-params">(<span class="hljs-keyword">size_t</span> n, <span class="hljs-keyword">size_t</span> d )</span> </span>{</span>
<span class="line"> d = <span class="hljs-built_in">std</span>::max(<span class="hljs-keyword">size_t</span>(<span class="hljs-number">1</span>), d);</span>
<span class="line"> n = <span class="hljs-built_in">std</span>::max(<span class="hljs-keyword">size_t</span>(<span class="hljs-number">1</span>), n);</span>
<span class="line"> <span class="hljs-keyword">double</span> r = <span class="hljs-number">1.0</span>;</span>
<span class="line"><span class="hljs-function"><span class="hljs-type">double</span> <span class="hljs-title">factorial</span><span class="hljs-params">(<span class="hljs-type">size_t</span> n, <span class="hljs-type">size_t</span> d )</span> </span>{</span>
<span class="line"> d = std::<span class="hljs-built_in">max</span>(<span class="hljs-built_in">size_t</span>(<span class="hljs-number">1</span>), d);</span>
<span class="line"> n = std::<span class="hljs-built_in">max</span>(<span class="hljs-built_in">size_t</span>(<span class="hljs-number">1</span>), n);</span>
<span class="line"> <span class="hljs-type">double</span> r = <span class="hljs-number">1.0</span>;</span>
<span class="line"> <span class="hljs-keyword">if</span> (n == d) {</span>
<span class="line"> <span class="hljs-comment">// intentionally left blank</span></span>
<span class="line"> } <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (n &gt; d) {</span>

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View File

@@ -51,45 +51,39 @@ namespace filament::backend {
DriverBase::DriverBase(const Platform::DriverConfig& driverConfig) noexcept
: mDriverConfig(driverConfig) {
if constexpr (UTILS_HAS_THREADING) {
// This thread services user callbacks
mServiceThread = std::thread([this]() {
JobSystem::setThreadName("ServiceThread");
do {
auto& serviceThreadCondition = mServiceThreadCondition;
auto& serviceThreadCallbackQueue = mServiceThreadCallbackQueue;
#if UTILS_HAS_THREADING
// This thread services user callbacks
mServiceThread = std::thread([this]() {
JobSystem::setThreadName("ServiceThread");
do {
auto& serviceThreadCondition = mServiceThreadCondition;
auto& serviceThreadCallbackQueue = mServiceThreadCallbackQueue;
// wait for some callbacks to dispatch
std::unique_lock<std::mutex> lock(mServiceThreadLock);
while (serviceThreadCallbackQueue.empty() && !mExitRequested) {
serviceThreadCondition.wait(lock);
}
if (mExitRequested) {
break;
}
// move the callbacks to a temporary vector
auto callbacks(std::move(serviceThreadCallbackQueue));
lock.unlock();
// and make sure to call them without our lock held
for (auto[handler, callback, user]: callbacks) {
handler->post(user, callback);
}
} while (true);
});
}
// wait for some callbacks to dispatch
std::unique_lock<std::mutex> lock(mServiceThreadLock);
while (serviceThreadCallbackQueue.empty() && !mExitRequested) {
serviceThreadCondition.wait(lock);
}
if (mExitRequested) {
break;
}
// move the callbacks to a temporary vector
auto callbacks(std::move(serviceThreadCallbackQueue));
lock.unlock();
// and make sure to call them without our lock held
for (auto[handler, callback, user]: callbacks) {
handler->post(user, callback);
}
} while (true);
});
#endif
}
DriverBase::~DriverBase() noexcept {
assert_invariant(mCallbacks.empty());
assert_invariant(mServiceThreadCallbackQueue.empty());
if constexpr (UTILS_HAS_THREADING) {
// quit our service thread
std::unique_lock<std::mutex> lock(mServiceThreadLock);
mExitRequested = true;
mServiceThreadCondition.notify_one();
lock.unlock();
mServiceThread.join();
}
#if UTILS_HAS_THREADING
stopServiceThread();
#endif
}
// ------------------------------------------------------------------------------------------------
@@ -113,11 +107,14 @@ void DriverBase::CallbackData::release(CallbackData* data) {
void DriverBase::scheduleCallback(CallbackHandler* handler, void* user, CallbackHandler::Callback callback) {
if (handler && UTILS_HAS_THREADING) {
#if UTILS_HAS_THREADING
if (handler) {
std::lock_guard<std::mutex> const lock(mServiceThreadLock);
mServiceThreadCallbackQueue.emplace_back(handler, callback, user);
mServiceThreadCondition.notify_one();
} else {
} else
#endif
{
std::lock_guard<std::mutex> const lock(mPurgeLock);
mCallbacks.emplace_back(user, callback);
}
@@ -185,6 +182,22 @@ void DriverBase::debugCommandEnd(CommandStream* cmds, bool synchronous,
}
}
#if UTILS_HAS_THREADING
void DriverBase::stopServiceThread() noexcept {
if (!mServiceThread.joinable()) {
return;
}
{
std::lock_guard<std::mutex> lock(mServiceThreadLock);
mExitRequested = true;
}
mServiceThreadCondition.notify_one();
mServiceThread.join();
assert_invariant(mServiceThreadCallbackQueue.empty());
}
#endif
size_t Driver::getElementTypeSize(ElementType type) noexcept {
switch (type) {
case ElementType::BYTE: return sizeof(int8_t);

View File

@@ -173,6 +173,8 @@ struct HwTimerQuery : public HwBase {
/*
* Base class of all Driver implementations
* If multithreading is supported, this class creates a `ServiceThread` responsible for executing
* user handlers.
*/
class DriverBase : public Driver {
@@ -236,17 +238,25 @@ protected:
void debugCommandBegin(CommandStream* cmds, bool synchronous, const char* methodName) noexcept override;
void debugCommandEnd(CommandStream* cmds, bool synchronous, const char* methodName) noexcept override;
#if UTILS_HAS_THREADING
// Stops the `ServiceThread`. This method is called during destruction but may be called
// explicitly if earlier shutdown is needed. This method is idempotent.
void stopServiceThread() noexcept;
#endif
private:
const Platform::DriverConfig mDriverConfig;
std::mutex mPurgeLock;
std::vector<std::pair<void*, CallbackHandler::Callback>> mCallbacks;
#if UTILS_HAS_THREADING
std::thread mServiceThread;
std::mutex mServiceThreadLock;
std::condition_variable mServiceThreadCondition;
std::vector<std::tuple<CallbackHandler*, CallbackHandler::Callback, void*>> mServiceThreadCallbackQueue;
bool mExitRequested = false;
#endif
};

View File

@@ -382,9 +382,18 @@ void OpenGLDriver::terminate() {
delete mCurrentPushConstants;
mCurrentPushConstants = nullptr;
// Flush all pending asynchronous tasks. Some tasks may end up posting follow-up operations to
// the `ServiceThread` (e.g., via CountdownCallbackHandler or any user-provided handlers). So we
// early stop the ServiceThread to ensure these are processed as well. Tasks posted to the main
// thread (due to no user handler) during this process are handled later by `Driver::purge`
// within `FEngine::shutdown`.
if (getJobWorker()) {
getJobWorker()->terminate();
}
#if UTILS_HAS_THREADING
stopServiceThread();
#endif
mContext.terminate();
mPlatform.terminate();
}

View File

@@ -705,6 +705,12 @@ void FEngine::shutdown() {
// Driver::terminate() has been called here.
}
// Handle any pending deferred destruction for asynchronous objects.
if (isAsynchronousModeEnabled()) {
gcDeferredAsyncObjectDestruction();
assert_invariant(mDeferredAsyncObjectDestruction.empty());
}
// Finally, call user callbacks that might have been scheduled.
// These callbacks CANNOT call driver APIs.
getDriver().purge();
@@ -755,7 +761,7 @@ void FEngine::prepare(DriverApi& driver) {
});
}
void FEngine::gc() {
void FEngine::gcManagers() {
// Note: this runs in a Job
auto& em = mEntityManager;
mRenderableManager.gc(em);
@@ -764,6 +770,21 @@ void FEngine::gc() {
mCameraManager.gc(*this, em);
}
void FEngine::gcDeferredAsyncObjectDestruction() {
if (mDeferredAsyncObjectDestruction.empty()) {
return;
}
auto it = std::remove_if(
mDeferredAsyncObjectDestruction.begin(),
mDeferredAsyncObjectDestruction.end(),
[](auto& f) {
return f(); // Returns true if it should be removed
}
);
// Actually erase the elements from the vector
mDeferredAsyncObjectDestruction.erase(it, mDeferredAsyncObjectDestruction.end());
}
void FEngine::submitFrame() {
if (isUboBatchingEnabled()) {
DriverApi& driver = getDriverApi();
@@ -1140,11 +1161,18 @@ bool FEngine::isValid(const T* ptr, ResourceList<T> const& list) const {
return l.find(ptr) != l.end();
}
template <typename T, typename = void>
struct HasIsCreationComplete : std::false_type {};
template <typename T>
struct HasIsCreationComplete<T, std::void_t<decltype(std::declval<T>().isCreationComplete())>>
: std::true_type {};
template<typename T>
UTILS_ALWAYS_INLINE
bool FEngine::terminateAndDestroy(const T* p, ResourceList<T>& list) {
if (p == nullptr) return true;
bool const success = list.remove(p);
bool FEngine::terminateAndDestroy(const T* ptr, ResourceList<T>& list) {
if (ptr == nullptr) return true;
bool const success = list.remove(ptr);
#if UTILS_HAS_RTTI
auto typeName = CallStack::typeName<T>();
@@ -1154,9 +1182,42 @@ bool FEngine::terminateAndDestroy(const T* p, ResourceList<T>& list) {
#endif
if (ASSERT_PRECONDITION_NON_FATAL(success,
"Object %s at %p doesn't exist (double free?)", typeNameCStr, p)) {
const_cast<T*>(p)->terminate(*this);
mHeapAllocator.destroy(const_cast<T*>(p));
"Object %s at %p doesn't exist (double free?)", typeNameCStr, ptr)) {
T* p = const_cast<T*>(ptr);
if constexpr (HasIsCreationComplete<T>::value) {
// The presence of 'isCreationComplete' in type T implies it supports asynchronous
// creation. For these asynchronous objects, we can terminate the backend resources
// immediately as they are no longer referenced. However, we defer the destruction of
// the frontend object if it's still being loaded.
// Reason: The creation process is still active and holds a reference to the frontend
// object to set `mCreationComplete` to true (see FTexture::FTexture). Deleting it now
// may cause a crash, so we wait until creation completes.
// Terminate the backend resource immediately as they're unnecessary from this point.
p->terminate(*this);
if (p->isCreationComplete()) {
// If creation is complete, we free the frontend object immediately. Note that in
// regular (non-async) mode, the `isCreationComplete` method always return true.
mHeapAllocator.destroy(p);
} else {
// We defer the destruction of the frontend object until the creation process
// completes. This ensures the object remains valid while the creation process still
// holds references to it.
mDeferredAsyncObjectDestruction.push_back([this, p]() {
if (!p->isCreationComplete()) {
return false;
}
mHeapAllocator.destroy(p);
return true;
});
}
} else {
p->terminate(*this);
mHeapAllocator.destroy(p);
}
}
return success;
}

View File

@@ -456,7 +456,8 @@ public:
}
void prepare(backend::DriverApi& driver);
void gc();
void gcManagers();
void gcDeferredAsyncObjectDestruction();
void submitFrame();
using ShaderContent = utils::FixedCapacityVector<uint8_t>;
@@ -586,7 +587,7 @@ private:
bool isValid(const T* ptr, ResourceList<T> const& list) const;
template<typename T>
bool terminateAndDestroy(const T* p, ResourceList<T>& list);
bool terminateAndDestroy(const T* ptr, ResourceList<T>& list);
template<typename T, typename Lock>
bool terminateAndDestroyLocked(Lock& lock, const T* p, ResourceList<T>& list);
@@ -708,6 +709,8 @@ private:
// Creation parameters
Config mConfig;
std::vector<std::function<bool()>> mDeferredAsyncObjectDestruction;
public:
// These are the debug properties used by FDebug.
// They're accessed directly by modules who need them.

View File

@@ -307,9 +307,14 @@ void FRenderer::skipFrame(uint64_t vsyncSteadyClockTimeNano) {
engine.flush(); // flush command stream
// Run the component managers' GC
auto& js = engine.getJobSystem();
js.runAndWait(jobs::createJob(js, nullptr, &FEngine::gc, &engine)); // gc all managers
// Run GC
JobSystem& js = engine.getJobSystem();
auto *rootJob = js.createJob();
js.run(jobs::createJob(js, rootJob, &FEngine::gcManagers, &engine)); // gc all component managers
if (engine.isAsynchronousModeEnabled()) {
js.run(jobs::createJob(js, rootJob, &FEngine::gcDeferredAsyncObjectDestruction, &engine));
}
js.runAndWait(rootJob);
mFrameSkipper.frameSkipped();
}
@@ -510,9 +515,14 @@ void FRenderer::endFrame() {
engine.flush(); // flush command stream
// Run the component managers' GC
auto& js = engine.getJobSystem();
js.runAndWait(jobs::createJob(js, nullptr, &FEngine::gc, &engine)); // gc all managers
// Run GC
JobSystem& js = engine.getJobSystem();
auto *rootJob = js.createJob();
js.run(jobs::createJob(js, rootJob, &FEngine::gcManagers, &engine)); // gc all component managers
if (engine.isAsynchronousModeEnabled()) {
js.run(jobs::createJob(js, rootJob, &FEngine::gcDeferredAsyncObjectDestruction, &engine));
}
js.runAndWait(rootJob);
}
void FRenderer::readPixels(